Problem: Simplify the following expression: $k = \dfrac{50gf - 50f^2}{40gf - 60f} + \dfrac{20gf + 60f^2}{40gf - 60f}$ You can assume $f,g,h \neq 0$.
Explanation: Since the expressions have the same denominator we simply combine the numerators: $k = \dfrac{50gf - 50f^2 + 20gf + 60f^2}{40gf - 60f}$ $k = \dfrac{70gf + 10f^2}{40gf - 60f}$ The numerator and denominator have a common factor of $10f$, so we can simplify $k = \dfrac{7g + f}{4g - 6}$